Whisk 2 1/4 cups all-purpose flour, 1 teaspoon baking powder, and 1 teaspoon salt together in a medium bowl.
Using a handheld electric mixer or a stand mixer with a paddle attachment, cream together 1 cup sugar and 3/4 cup butter together on medium-high speed for 3 to 5 minutes, or, until light and fluffy. Add 3 eggs, one at a time, scraping down the sides of the bowl after each addition, then stir in 1 tablespoon vanilla extract.
Add the flour mixture (from the first step) and use a rubber spatula to stir until a smooth dough forms. Wrap the dough in plastic wrap, flatten into a 1-inch thick disk, and freeze for 30 minutes.
Preheat the oven to 375 (F). Butter (or, use cooking spray) a shallow 10-inch round baking pan or tart pan.
Divide the dough into two equal portions and pat one portion evenly into the bottom of the prepared pan.
Spread 2 1/2 cups of fruit evenly over the dough.
Break the remainder of the dough into tablespoon-sized pieces (I used a 1-tablespoon sized cookie scoop for this part) and distribute atop the fruit. Sprinkle 1 tablespoon turbinado sugar over the dessert.
Bake for 30-40 minutes in the preheated oven, or until lightly golden and firm. Cool for 30 minutes on a wire rack before serving.